Mathematics for Management -- Supplementary Electronic Materials

Quiz: Functional Models

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1. The first, second and fourth terms of a direct proportion are \(16\), \(24\), and \(54\) respectively. Then the third term is:

\( 36 \) \( 28 \) \( 48 \) \( 32 \)

2. If \(12\), \(21\), \(72\), \(126\) are in direct proportion, then:

\( 12 \cdot 21 = 72 \cdot 126 \) \( 12 \cdot 72 = 21 \cdot 126 \) \( 12 \cdot 126 = 21 \cdot 72 \) none of these

3. If \(x\), \(y\) and \(z\) are in direct proportion, then:

\( \frac{x:y}{z:x} \) \( \frac{x:y}{y:z} \) \( \frac{x:y}{z:y} \) \( \frac{x:z}{y:z} \)

4. The demand and supply functions are given, respectively, by the equations: \(P = 20 - 0.02 Q\) and \(P = - 12 + 0.06 Q\). The equilibrium price and quantity are given by:

\( P = 12\), \(Q = 7200 \) \( P = 20\), \(Q = 1000 \) \( P = 400\), \(Q = 12 \) \( P = 12\), \(Q = 400 \)

5. The demand and supply functions are given, respectively, by the equations: \(Q_d = 10 - P\) and \(Q_s = 3P - 2\). The coordinates of the equilibrium point \((P_e, Q_e)\) are given by:

\( (6,4) \) \( (5,5) \) \( (7,3) \) \( (3,7) \)

6. The supply function for a product is given by: \(Q_s = 3P - 4\). A unit tax \(t\) is then imposed on the supplier. The new supply function becomes:

\( Q^*_s = 3P - 4 + t \) \( Q^*_s = 3(P-t) - 4 \) \( Q^*_s = 3P - 4 - 3t \) \( Q^*_s = 3P - 4 - t \)

7. An industry is selling a product for \(10\) GEL per unit. The fixed cost for assets is \(40000\) GEL with variable cost of \(6\) GEL per unit. How many units should be produced to break even?

\( 8000 \) \( 10000 \) \( 12000 \) \( 14000 \)

8. The data for an industrial unit is as follow: \(20\) GEL selling price per unit, \(15\) GEL variable costs and \(85000\) GEL fixed costs. Find the break-even point in units.

\( 4250 \) \( 17000 \) \( 5667 \) \( 15567 \)

9. Fixed costs for desk lamps are \(280000\) GEL. The variable cost per unit is \(17\) GEL, and the selling price per unit is \(35\) GEL. Find the break-even point in terms of sales GEL.

\( 15556 \) \( 264452 \) \( 544444 \) \( 279982 \)

10. Research on a new product indicates that the product can be sold for \(30\) GEL per unit. Cost analysis provides the following information: \(5640\) GEL fixed cost per period, \(20\) GEL variable cost per unit, and \(800\) units production capacity per period. What is the cost function, where \(X\) denotes the number of units?

\( C = 5640 + 20X \) \( C = 800 + 20X \) \( C = 5640 + 800X \) \( C = 5640 + 30X \)

Your grade is: __ of 10

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Solution: 1a; 2c; 3b; 4d; 5d; 6d; 7b; 8b; 9a; 10a

Here, a, b, c, d indicate the 1st, 2nd, 3rd, and 4th answer choice, respectively, for the numbered questions.